Quantum Field Theory in the Light of Distribution Analysis

It is shown that part of the divergences and ambiguities of the current quantum theory of fields can be overcome by the consistent use of distribution analysis. Representing the singular functions of field theory by distributions, nongauge invariant and nonequivalent terms will be eliminated from the $S$-matrix in renormalizable as well as in nonrenormalizable theories without any limiting process. Instead of divergent quantities, there appear arbitrary normalization and division constants. Feynman's cutoff as well as the renormalization are automatically contained in a theory which gives a correct meaning to delta-functions. Applications to closed loop processes are discussed in detail. It is not possible to attribute definite values to the parameters of bare particles; for that, some modifications of the theory seem to be necessary.